Question: Omar is 2 times as old as Ben. Fourteen years ago, Omar was 9 times as old as Ben. How old is Omar now?
Explanation: We can use the given information to write down two equations that describe the ages of Omar and Ben. Let Omar's current age be $o$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $o = 2b$ Fourteen years ago, Omar was $o - 14$ years old, and Ben was $b - 14$ years old. The information in the second sentence can be expressed in the following equation: $o - 14 = 9(b - 14)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = o / 2$ . Substituting this into our second equation, we get: $o - 14 = 9($ $(o / 2)$ $- 14)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 14 = \dfrac{9}{2} o - 126$ Solving for $o$ , we get: $\dfrac{7}{2} o = 112$ $o = \dfrac{2}{7} \cdot 112 = 32$.